United Nations Headquarters was fired upon yesterday with a 3.5-inch bazooka from across the East River. The attack coincided with a demonstration by anti-Communist Cubans at the front entrance against the presence of Maj. Ernesto Che Guevara of Cuba.

A single shell from the bazooka, a portable rocket launcher used by the Army, arced across the river from Queens and fell harmlessly about 200 yards from the shore. The blast sent up a geyser of water and rattled windows in the headquarters just as Major Guevara, Havana's Minister of Industry, was denouncing the United States.

Shortly before, a hysterical woman brandishing a hunting knife with a seven-inch blade detached herself from 50 anti-Guevara pickets and tried to force her way into the front entrance. The police subdued the leather-jacketed woman, and later quoted her as saying she intended to assassinate Major Guevara.

In the sealed-off General Assembly Hall, the blast was clearly heard over the voice of Major Guevara, who was assailing United States foreign policy and rejecting a denuclearization pact for the Western Hemisphere.

He paused not a moment in his speech. Later, strolling through the delegates' lounge in his green fatigue uniform and highly polished black boots, he said, with a languid wave of his cigar, that the explosion "has given the whole thing more flavor."

But the police saw no humor in the incident. Had the rocket shell crashed against the glass-and-concrete facade of the headquarters building, there would almost certainly have been casualties. The rocket launcher was found abandoned directly opposite the United Nations in a weed-strewn lot on the east bank of the East River. The device consisted of a tube about three feet long which was bound by ropes to a crate filled with ballast. It had a sighting device, which, according to the police, was fixed on the misty silhouette of the 38-story United Nations Headquarters.

It was fired, apparently by a clock-like device, at 12:10 P.M. At that time a noisy demonstration in front of the United Nations Headquarters was at a peak of tension. The crowd of Cuban exiles was hurtling curses at the police, who, at the time were carrying away Molly Gonzales, the woman who said she wanted to cut down Major Guevara with a hunting knife.

The explosion and the outcry of the crowd marked one of the wildest episodes since the United Nations moved into its East River headquarters in 1952.

Inside the massive glass structure most United Nations personnel thought that the explosion had occurred in front of the building, and that a bomb had been thrown by one of the demonstrators in United Nations Plaza. Few chanced to see the spout of water in the river off West 43^rd Street.

Few knew that the building, at that moment, was under attack from both front and rear.

Could the rocket attack have been a diversion, under cover of which assassins might have stormed the front entrance and reached Major Guevara.

The police scoffed at this suggestion. They said the attacks were "purely coincidental."

The stormy episode did not end with the dragging away of Miss Gonzales. Later, three men succeeded in cutting down the Soviet flag from its pole in front of the United Nations building. United Nations guards quickly hoisted it again, but the official Soviet press agency Tass described the incident as "a new provocation," carried out "with the connivance of the New York City police."

Miss Gonzales, a short, stocky woman clad in tight black slacks and a synthetic black leather jacket, was charged with felonious assault, resisting arrest, and violation of the Sullivan Law.

She was spotted by Patrolman Robert Connolly, who saw her dash along the sidewalk on 43d Street, leap over a 2 ½-foot hedge-and-wire fence and run across the United Nations grounds towards a four-foot wall.

Patrolman Connolly gave chase and was joined by Patrolman Michael Marino, who yelled: "Watch her, she has a knife."

The woman waved a knife at Patrolman Marino, but he dodged it. There was a scuffle, and Miss Gonzales and the two policeman fell to the ground. Before she was subdued, Patrolman Connolly was scratched under both eyes, and Marino suffered scratches on the hand and bruises on the left leg. Both were treated at St. Clare's Hospital.

The woman had been screaming "Arriba,"Spanish of "Hail!" Later she was quoted by the police saying: "The knife was meant for Guevara. I meant no harm to the policemen."

Later, when Major Guevara learned that his would-be assailant was a woman, he forgave her and remarked: "It is better to be killed by a woman with a knife than by a man with a gun."

Mayor Wagner ordered a full police investigation of the attacks. He assured Ambassador Adlai E. Stevenson, permanent United States delegate to United Nations, that everything possible would be done to find who launched the rocket attack.

The police meanwhile were able to find only a handful of persons who said they saw they launching of the missile.

The witnesses were Capt. Anthony A. Saganski and the four-man crew of the tugboat Sandy Hook, of the Central Railroad of New Jersey.

"I was coming down river with a railroad car barge on either side of me," he said. "I was looking toward Long Island City when I saw a puff of smoke down by the shore.

"A flock of seagulls flew up in the air and a second later I heard a small report.

"Then off to my right, I heard a big blast. I didn't look at that because I figured the puff of smoke was where the explosion started.

"I didn't see anybody at the spot where I saw the smoke. I didn't see anybody run away. I was about 400 or 500 feet off shore.

"I proceeded slowly down river until a police helicopter flew overhead and ordered me to a pier off Jackson Street [Manhattan]. Several patrolmen from a police launch boarded me before I got in."

Captain Saganski was questioned for 30 minutes, then allowed to proceed to Jersey City.

Meanwhile, three workers in the Long Island Rail Road yard at 48^th Avenue, Long Island City, found the rocker launcher. They had heard radio reports of the river explosion and recalling a noise they had heard shortly before noon in a nearby lot, initiated a search. Some 90 minutes after the explosion, they came upon the weapon in the rear of Adam Metal Supply Company.

A Cuban flag was tied to it.

In the office of the metal supply company, Claude Pollet, a 41-year-old truck driver, recalled one of the railroad workers having burst into the room shouting, "A pipe is sticking up out there that fired the shot."

"A friend and I ran out of the office to look for the weapon," Mr. Pollet continued. "We walked out to a point of land beyond the warehouse and saw nothing. We decided this guy was crazy or a nut.

"Then as we walked back to the office we saw it, about 150 feet from the water's edge. It looked like a black pipe with white strings. It looked like some kind of home-made mortar."

The first detective to reach the scene, William Reilly, of 108^th Precinct, Queens, thought it was a sawed-off bazooka. "If you looked through the sight you could see the United Nations Building," he said.

"The thing also had a timing mechanism, something like a clock, in a box eight inches long, four and one-half inches wide, three inches deep, and made of metal - the size of a cereal box."

The bomb squad removed the device after it had been dusted for fingerprints. Later it was turned over to the Army at Fort Tilden, Queens, for further identification.

Lieut. Kenneth W. O'Neil, commander of the bomb squad, said the rocket launcher was made in the United States for the use of the Armed Forces.

He said the pipe was originally olive drab, but had been painted black.

The weapon was officially described as a bazooka. A bazooka is a light and portable crew-served weapon that consists of a smooth-bore firing tube, open at both ends, used to fire armor-piercing rockets. The weapon is normally fired from the shoulder.

The version used in yesterday's attack was at first described as a mortar, perhaps because it had been rigged to a wooden crate on the ground.

A mortar, however, is a short, muzzle-loading cannon with either a rifled of smooth bore that is emplaced on the ground or some other hard surface and used to lob projectiles at high angles.

Unlike the bazooka, the mortar is closed at the base. The gunner drops the shell down the muzzle, and it is detonated by a firing pin that projects upward from the base.

Investigation by the bomb squad proved that the weapon had been fired during the day, thus convincing the squad that it was the device that fired at the United Nations.

The East River is about 900 yards wide at the United Nations, and a member of the bomb-squad said the launching weapon had sufficient range to send a projectile crashing into the building. He said the shell fell short and exploded in the river apparently weighed eight pounds, was perhaps 18 inches long, and may have contained 1.9 pounds of a high explosive called "composition B."

He said that if the shell had passed though a window and exploded in a room, people in the room probably would have been killed.

The arc of the missile must have passed close to Belmont Island, a small rocky island that contains only a navigation light. The police searched it without finding clues. The expressed doubt that the shell would be recovered from the river.

Last night the bomb squad announced that "several" serial numbers had been found on the weapon. They were trying to trace the numbers to various arsenals.

The weapon was of a type usually fired by two men, a bomb squad expert said. The timing device enabled it to be fired at a predetermined time without anyone's being in the Ling Island City lot at that moment.

The shell landed in the East River with two blocks of the BMT Queensboro subway tube but ther was no damage to the tunnel.

The "siege" of United Nations had begun with a bit of psychological warfare.

At 10:30 A.M. an anonymous telephone call was received at the police communications center. A man's voice, with a Latin-American accent, said: "I have put a bomb in front of the U.N. building. Keep people away between 11:30 and 12:30 P.M. Long live Cuba."

A police search of the area was under way at the moment the mortar shell exploded in the river.

The arrival of the bearded Major Guevara on Wednesday had resulted in heavy police patrolling of the United Nations.

At 6:45 A.M., the Federal Bureau of Investigation had cautioned the New York police against a possible bomb scare or bomb activity later in the day at the United Nations.

When Miss Gonzales, first identified as Gladys Perez, was booked at the East 51^st Street station she gave several false names. She finally admitted she was Molly Gonzales, 24 years old of 6040 Park Avenue, West New York, N. J. She said she had come form Santa Cruz, Cuba, two years ago. She was charged with felonious assault on a police officer and possession of a knife. She will be arraigned today in Part IA of the New York Criminal Courts.

She carried in a paper bag a bottle of detergent and about 500 carpet tacks, for which she gave not explanation.

Picketing of the United Nations Headquarters continued until 7:25 P.M., when the police told some 20 pickets that Major Guevara had left the grounds by a side gate. The picket then dispersed.

They had milled about with signs reading "Invade Cuba Now" and "Guevara, get out of Cuba."

Later, eight demonstrators, who described themselves as Cuban exiles, showed up at the Cuba mission at 6 East Sixty-Seventh Street. They carried signs protesting the appearance of Major Guevara at the United Nations. One bore a fire extinguisher and a placard that read, "We pretend to exterminate Guevara for what he said in the U.N. today."

The police had barricaded both sides of 67^th Street and a part of Fifth Avenue. They kept demonstrators behind wooden barriers 300 feet from the mission.

Members of the bomb squad examined with a fluorescent device all packages arriving at the mission.

Major Guevara arrived at the mission shortly before 7:30 P.M. in a limousine and was greeted by jeers and catcalls. Several pickets yelled in Spanish: "Assassin!" The major ignored them. After he disappeared inside the building, the pickets sang the Cuban national anthem.

The three men who figured in the incident involving the Soviet flag at United Nations Plaza were paroled for a hearing Thursday for disorderly conduct charges. They were identified as Enrique Castro, 28, of 48-10 45^th Street, Woodside, Queens; Medara Rodriguez, 21, unemployed, of 124 Fort George Avenue, and Carlos Vardes, 28, of 740 Gun Hill Road, the Bronx.

The police said Mr. Castro and Mr. Rodriguez had pulled down the flag while Mr. Vardes tried to block traffic in the plaza. All three were booked at the East 51^st Street Station on a charge of disorderly conduct.

Nikolai T. Fedorenko, Soviet Chief delegate, reacted angrily to the flag incident.

"We are among pirates," he told reporters last night at a diplomatic reception. "There is no protection. How can we work?"

He said he was thinking of making an official protest. "It has never been permitted to treat a national flag in such a way," he continued. "I ask, What is going on? Where do we stand! What are we doing?"

The shelling of the United Nations drew sympathetic comment form Pedro Pena Gongora, national secretary general of the White Rose Cuban exile movement.

"I'm sorry they didn't hit him [Major Guevara]," Mr. Pena Gongora said.

"He's an Argentinian; he's not even a Cuban. Imagine him coming to the United States to represent our country. We resent him more because he's an Argentinian than because he's a Communist. A guy like that - they don't want him in his own country."

Mr. Pena Gongora said he could not imagine who might have launched the shell.